MathDB

12nd ibmo - mexico 1997/q5.

Source: Spanish Communities

April 22, 2006

geometrycircumcircletrapezoidparallelogramvectortrigonometryangle bisector

Problem Statement

In an acute triangle

\triangle{ABC}

, let

AE

and

BF

be highs of it, and

H

its orthocenter. The symmetric line of

AE

with respect to the angle bisector of

\sphericalangle{A}

and the symmetric line of

BF

with respect to the angle bisector of

\sphericalangle{B}

intersect each other on the point

O

. The lines

AE

and

AO

intersect again the circuncircle to

\triangle{ABC}

on the points

M

and

N

respectively.
Let

P

be the intersection of

BC

with

HN

;

R

the intersection of

BC

with

OM

; and

S

the intersection of

HR

with

OP

. Show that

AHSO

is a paralelogram.

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